Recently, the technology for measuring small displacement of the object in a noncontact way as an indication of which a pattern or a texture having a random structure spatially such as a laser speckle pattern and a random dot pattern has been noted. In particular, this technology occupies an important position in the industrial application fields such as a non-destructive inspection and a material strength examination.
Conventionally, displacement sensing of the spatial pattern having the random structure has been operated by following methods according to the above-mentioned background. That is, the first method is a method to take a picture of a light intensity distribution of the pattern respectively with a camera before and after giving displacement, calculate a cross-correlation function directly in the spatial signal domain of this light intensity distribution, and obtain the direction of displacement and the displacement magnitude from the peak position. The second method is a method to perform the mathematical process equivalent to the above-mentioned method completely in the spatial frequency domain. In other words, the above-mentioned method is a method to execute a Fourier transform of two spatial patterns after and before the displacement respectively, select another complex conjugate of the obtained spatial frequency spectrum, create a composite spectrum to cross this on the other hand, and to further execute an inverse Fourier transform for this and obtain the cross-correlation function.
However, since the cross-correlation function obtained by using the above-mentioned two methods is basically an intensity correlation function calculated directly from the light intensity distribution of the spatial pattern itself, there is a problem of being susceptible to the influence of a nonlinearity characterization of the sensibility of the camera to detect the light intensity and a quantum noise easily.
On the other hand, in the field of a communication theory, it is known that the phase information is more robust than the intensity information of the signal to the nonlinearity characteristic of the detector and the quantization noise. This means that it is possible to improve the performance of a displacement measuring apparatus if the phase information of the signal is used instead of the conventional correlation function using the intensity information directly in order to calculate the correlation function.
The phase-only correlation method disclosed in “patent document 1” listed below is well-known as the calculation method of the correlation function using such the phase information. This method is a method to control the amplitude of the above-mentioned composite spectrum which is complex function according to making constantly or a logarithmic transform, etc., create an amplitude-limited complex composite spectrum which consists only from the phase information, execute an inverse Fourier transform for this, and obtain the cross-correlation function.
[Patent document 1] Japanese patent Publication No. 3035654.